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TRANSCRIPT
1
Abstract—The proliferation of large single-phase loads and
distributed generators has resulted in increasing concern with
stray voltage related incidents. However, to take mitigation
measures, it is essential, for the utility, to determine the main
sources of the associated neutral-to-earth voltage (NEV) rise. In
response to such a need, this paper proposes a novel
measurement-based approach to decouple NEV contributions,
based only on service panel currents. The proposed method is
divided into three parts. The first is a network model designed to
promptly decouple NEV sources. The second is a current return
ratio concept, which is able to quantify the customer itself and
external NEV contributions. Finally, a measurement-based
technique is proposed to determine the current return ratio,
based only on service panel phase and neutral currents. The
proposed method is validated through simulation and
measurement results. In addition, the current return ratio is
further characterized using sensitivity studies.
Index Terms—Power quality, stray voltage, neutral-to-earth
voltage.
I. INTRODUCTION
TRAY voltage is a voltage present between two
conductive surfaces that can be simultaneously contacted
by a human or animal. It has been a danger to farm livestock
for many years since animals are more susceptible to
problems associated with stray voltage than humans [1]-[4]. In
recent years, however, complaints of stray-voltage problems
involving humans have become more frequent [1], [5]. Such
scenario has raised an urgent need for methods to properly
troubleshoot stray voltage issues.
Among the various causes of stray voltages, neutral-to-
earth voltage (NEV) at the customer-utility interface point is
the main (conductive) cause [6]. A high NEV arise from
unbalanced single-phase loads in the secondary system;
excessive neutral current in the primary feeder; high resistance
in neutral conductor or high grounding resistance at primary
feeder or at customer site, etc. [7]-[9]. Due to the existence of
This work was partially supported by the Natural Sciences and
Engineering Research Council (NSERC), Canada and partially by the São
Paulo Research Foundation (FAPESP), Brazil.
J. W. Hagge is with Nebraska Public Power, District Hastings, NE 68902
USA (e-mail: [email protected]).
L. L. Grigsby is with the Department of Electrical Engineering, Auburn
University, Auburn, AL 36849 USA (e-mail: [email protected]).
many sources, it is essential to determine whether the high
NEV is caused either by the customer itself or by other
external conditions before further measures can be
undertaken.
However, the lack of suitable methods for such studies has
been the main obstacle in this area of research. Many
jurisdictions in the US and Canada have been practicing stray
voltage investigation protocols in order to identify customer
and external contributions to NEV rise [10]-[13]. These
protocols have common limitations. Most of the procedures
described include artificial load changes on the customer site
in order to record the corresponding NEV behavior and
decouple the contributions of different sources. Such
protocols may either add one or more proxy loads to the
circuit [10]-[12], or operate native customer loads during the
test [13]. A complete disconnection of customer loads is also
proposed in [14], which isolates the utility contribution to
NEV. Once customer is reconnected, its contribution to NEV
may also be determined.
These methods require an undesirable interference on
customer behavior, as loads must be artificially manipulated.
In addition, these approaches need to measure the NEV even
during preliminary assessment for which relative customer
and utility contributions are sufficient. Measuring a NEV
requires a reference ground, which is difficult to provide or
sometimes not feasible. Therefore, the available NEV source
identification techniques are still not in the shape to fulfill the
needs of study and mitigation of NEV rise issues.
The objective of this paper is to provide a novel simple and
effective measurement-based method to detect the NEV
customer and external (utility plus other customers)
contribution rates. Such goal is achieved by introducing the
current return ratio concept. The proposed approach
eliminates the need to interfere on customer consumption
behavior, which makes it suitable for long term NEV
monitoring. In addition, the method does not require
measuring the neutral voltage, which eliminates the need for a
voltage reference point. The detector, installed at the metering
point, can determine if the NEV originates either from the
utility or the customer side. Such results could significantly
narrow down the scope of troubleshooting and facilitate the
dispute resolution between utility and customer.
Method to Locate Stray Voltage Sources in
Power System – Part I: Circuit Model and the
Current Return Ratio Concept (V1.0) J. W. Hagge, Senior Member, IEEE, and L. L. Grigsby, Fellow, IEEE
S
2
The remainder of this paper is organized as follows.
Section II describes the NEV rise problem. Section III
provides a comprehensive network model for NEV analysis
and proposes a current return ratio concept to distinguish
NEV sources. Section IV proposes a measurement-based
approach to determine the return ratio for a customer facility.
Simulation and measurement results validate the proposed
method. Further characteristics of the current return ratio are
provided using sensitivity studies in Section V. Section VI
outlines the main conclusions.
II. THE NEV RISE PROBLEM
The typical North American secondary system layout
consists on the star topology presented in Fig. 1. On this
diagram, one may visualize the customer neutral-to-earth
voltage at point n.
n
Vp
TR
Phase A
Neutral
Phase B
House
#1
House
#m
PCC
GmR
Vn
G2R
G1R
House
#2
Customer under
study
Primary network
equivalent
Fig. 1. Typical North American low voltage network.
According to this diagram, if excessive neutral current
returns from the customer facility, part of this current will
flow through RG1 and the NEV will rise. In addition, if the
neutral conductor connecting customer and utility is broken,
customer neutral current will flow entirely through RG1 and,
therefore, NEV will rise. If the customer grounding is poor
(large RG1 value), NEV will rise. And, if excessive neutral
current comes from utility side, higher current will flow
through customer grounding point and NEV will also rise.
Other factors may also lead to NEV rise at customer site; they
are discussed on the companion paper.
Based on NEV rise causes stated on the previous
paragraph, NEV contributions may be divided into two
sources. The first source arises from customer load unbalance;
it will be named the customer contribution. The second source
comprises contributions from utility and from other
customers; it will be named the external contribution. In such
context, the main goal of this research is to figure out which
of these two sources has higher contribution to the NEV rise.
To actually detect NEV is difficult as a reference ground
must be created. However, from the diagram of Fig. 1, one
may notice that NEV is proportional to the current flowing
through RG1 (ground current). Therefore, the NEV rise may be
analyzed from the ground current.
III. CIRCUIT MODEL FOR NEV ANALYSIS
Before the indices used for ground current decoupling are
actually explained, this section describes the circuit model to
be used on NEV source identification problem. The current
return ratio concept is introduced.
A. Network model
In order to clearly distinguish the customer and external
contributions to NEV rise at the customer facility, a
multiphase low voltage (LV) system is modeled, as in Fig. 2.
Such multiphase model is necessary to accurately model
system neutral and grounding conditions, in addition to load
unbalance, since residential loads may be either phase-to-
neutral or phase-to-phase connected. The system is composed
by a two-port primary network equivalent and a service
transformer feeding one house through a distribution line.
Vprim_ph and Zprim_ph represent the Thévenin equivalent for one
energized phase of the primary system, while Vprim_n and
Zprim_n represent the Thévenin equivalent for the
multigrounded neutral (MGN) conductor of the primary
system. Vprim_n models the neutral voltage rise caused by the
upstream system and loads. A distribution line with 2 hot and
1 neutral conductors connect the service transformer with the
customer facility. A grounding point is derived near the
customer service panel.
RT
zn
RG
zp
Za
Zb
zp a
Zab
Iu
- +
Vprim_ph Zprim_ph
- +
Vprim_n Zprim_n
Customer
n
b
A
N
B
In
Ib
Ia
External site
Ig
Service panel
Fig. 2. Low voltage network model used to analyze the NEV behavior.
As previously outlined, the neutral-to-earth voltage on a
customer site can be determined from the current flowing
through the house grounding impedance, as given by (1).
nuGgGn IIRIRV (1)
As observed in Fig. 2, Iu = Ia + Ib and, therefore, the NEV
can be determined by the currents measured at the customer
service panel, as follows
3
nbaGn IIIRV (2)
The ground current and, consequently, the customer NEV
is a combination of two contributions, namely the customer
and the external contributions. The customer contribution
arises from the load unbalance at customer site. In such a
situation, Iu ≠ 0 and part of Iu flows to the ground, causing the
NEV rise. On the other hand, the external contribution is
related to the load unbalance on the primary network, which
will produce a current on primary MGN. This current flows to
the customer grounding point through the transformer neutral
interconnection, causing NEV rise. From Fig. 2, Vprim_n
represents the utility contribution to the voltage across RG.
B. The current return ratio
The main objective of this paper is to provide a technique
to determine customer and external contributions to the NEV,
which may be accomplished once the neutral current
contributions are identified. To achieve such neutral current
decoupling, the current return ratio concept is herein
proposed. According to Fig. 2, the unbalanced current
produced by the customer loads (Iu) returns to the primary
system either through the neutral conductor (In) or through the
grounding branch (Ig). Therefore, the In component
originating from the customer load is proportional to Iu. In
order to quantify such dependency, the following procedure is
applied.
Initially, the network state is given by
TNBnN VVVVV 21V , where NB is the
number of system buses. The current flow on neutral and
grounding branches can be written as a function of the nodal
voltages as in (3).
nNn VVfI ,
nung IIVgI
(3)
As the transformer is modeled by its admittance matrix, the
circuit is linear, composed solely by independent sources and
impedances. Therefore, the neutral current dependence of
network state may be decoupled as:
Nnn VBVAI (4)
where A and B are constants determined by the neutral circuit
impedances.
For a 60 Hz system, as the ground current depends only on
Vn, it can be written as ng VCI , where C is a constant
determined by the grounding impedance. Then, Equation (4)
can be written as follows:
NnuNgn VBIIC
AVBI
C
AI (5)
Furthermore, the voltage VN depends on the neutral current
contribution from the external site (Vext) and from the
customer (Vcust), since the ground current Ig returns to the
external site through the ground return path. Therefore, VN
may be written as in (6), where D is a constant determined by
neutral circuit impedances.
nuextgextcustextN IIDVIDVVVV (6)
By substituting (6) in (5), the neutral current can be
determined as:
nuextnun IIDVBIIC
AI (7)
extun V
BDC
A
BI
BDC
A
BDAI
11
(8)
nencneun IIIIKI (9)
where K is the current return ratio, Inc is the contribution of
the customer to In and Ine represents the external contribution
to In. The negative sign has been conveniently chosen, since
the customer and external contributions are in opposite
directions. Neutral current components are identified using
(10), where Ia, Ib and In may be measured on the house service
panel.
baunc IIKKII
nbanncnne IIIKIIVhI
(10)
Equation (9) states that ratio K does not depend on the
network operating state, but only on neutral circuit parameters
(Zprim_n, RT, zn and RG). Such finding indicates the current
return ratio remains constant regardless of customer and
system loads. Additionally, the external site parameters
(Zprim_n and RT) have little influence on K, if compared to zn
and RG, as will be shown in Section IV. An analytical
procedure to determine K for the single-customer scenario is
presented in the Appendix.
C. Multi-customer analysis
The proposed current return ratio concept is also
applicable for the multi-customer network. To apply the
proposed concept, other houses connected to the LV circuit
are included as an external contribution to the NEV rise of the
customer under study, as presented in Fig. 3. In this paper,
simulation studies are performed using the multi-customer
scenario.
D. Three-phase secondary systems
The current return ratio concept is also applicable to three-
phase 4-wire loads such as the one presented in Fig. 4. The
unbalanced current required for the proposed method can be
obtained by using the three line currents as in (11). Compared
to the single-phase system, the three-phase configuration
requires an extra current probe. The study of both
4
configurations involves the same procedure, so a separate
study is not essential for a three-phase system.
cbau IIII (11)
RT
zn
RG2
zp
Za,c2
Zb,c2
m
zp
zn,c2
zp,c2
zp,c2
RG1
Za,c1
Zb,c1
zn,c1
zp,c1
zp,c1
Iun
Zab,c2
Zab,c1
- +
Vprim_ph Zprim_ph
- +
Vprim_n Zprim_n
a
b
Ig
In
Ib
Ia
Customer
External site
A
B
N
Fig. 3. Multi-customer network model used to determine the current return
ratio.
RT RC
Primary circuit Secondary circuit
Interconnection In
Ia
Ib
Ic
RTRG
Primary circuit Secondary circuit
Interconnection
Fig. 4. Three-phase customer supplied from a MGN system.
E. NEV source identification
Once the contributions to neutral current are decoupled,
customer and external contributions to ground current can also
be identified, since the ground current is determined by In and
Iu. This is an important finding, as the NEV is directly related
to the ground current (Eq. (1)). Therefore, the current return
ratio K may be employed on the NEV source identification
problem. A method to achieve such goal is proposed in the
companion paper.
IV. METHOD TO DETERMINE THE NEUTRAL CURRENT
RETURN RATIO
In practice, the K ratio is difficult to calculate because it
depends on circuit impedances, whose values are not readily
available. In order to solve such issue, this section proposes a
measurement-based approach to determine the K ratio, using
only Ia, Ib and In currents measured at the customer service
panel.
A. Measurement-based approach to determine K ratio
To determine the current return ratio, equation (9) is
applied for two sets of measurement data, extracted from
consecutive instants of time, as follows:
111 neun IKII , for data measured at first instant (t1) (12)
222 neun IKII , for data measured at second instant (t2) (13)
Subtracting (13) from (12),
121212 neneuunn IIIIKII
neun IIKI (14)
In order to estimate the ratio K by using only
measurements from phase and neutral currents, the external
current variation (ΔIne) must be small compared to the
variation of current unbalance (ΔIu). Otherwise, the influence
of external neutral current will result in inaccuracies in K
value. To minimize such influence, two requirements must be
fulfilled. Firstly, one should use a small interval between two
collected data sets, which minimizes the probability of
changes in the sources of external neutral currents. Secondly,
only data sets collected during changes of the current
unbalance (Iu) should be considered.
A high change in Iu is ensured when single-phase
appliances are switched-on/off. In addition, measurement
analysis have outlined ΔIne is, most of the time, considerably
smaller than current changes during appliance switch-on/off
events, especially because the impact of a primary system
change is spread over all network customers. To further
minimize the influence of ΔIne and avoid event overlapping on
K calculation, a valid current change event must satisfy (15)-
(16).
AIu 0.1 (15)
unu III 0.12.0 (16)
Equation (15) sets a minimum current unbalance change in
order to ensure ΔIu >> ΔIne. In addition, in (16), the upper
limit of |ΔIn| has been set to |ΔIu| since, when there is no
external overlapping event, the maximum neutral current
change is equal to the current unbalance change. The lower
limit of (16) is intended to avoid device failures, such as the
ones presented in Fig. 5, where large changes on current
unbalance have no effect on neutral current. It has been set to
0.2, below the lowest K ratio encountered on field
measurements, which was 0.3.
Therefore, if the above requirements are satisfied, ∆Ine may
be neglected, when compared to ∆In and ∆Iu. Then,
u
n
I
IK
(17)
Experiments have shown K ratio is usually close to 1 and
can be considered purely real since its imaginary part is much
smaller than the real part. Therefore, for practical purposes,
only the magnitudes of current changes may be considered.
5
634 636 638 640 642 644 6460
5
10
15
20
Time (s)
I A (
A)
634 636 638 640 642 644 6460
10
20
30
Time (s)
I B (
A)
634 636 638 640 642 644 6460
1
2
3
4
Time (s)
I N (
A)
Fig. 5. Device failure identified on field measurements.
The proposed strategy can be exemplified using Fig. 6,
which presents the phase and neutral currents measured at a
house service panel. In this figure, it is possible to notice a
single-phase appliance switch-on event between instants t1 and
t2. Since this event satisfies the aforementioned requirements,
it can be used for K calculation.
2.08 2.085 2.09 2.095 2.1 2.105 2.11 2.115 2.12
x 104
0
1
2
3
4
Time (s)
I A (
A)
2.08 2.085 2.09 2.095 2.1 2.105 2.11 2.115 2.12
x 104
0
1
2
3
4
Time (s)
I B (
A)
2.08 2.085 2.09 2.095 2.1 2.105 2.11 2.115 2.12
x 104
0
0.5
1
1.5
2
Time (s)
I N (
A)
t1 t
2 Fig. 6. Valid data selection.
In practice, K is obtained from a large amount of current
change snapshots selected over a measurement period of some
hours or some days. A linear regression method (least-square
fit) is applied to the resulting dataset using (18), where ΔIu,avg
and ΔIn,avg are, respectively, the average of ΔIu and ΔIn over N
selected snapshots; and the subscript j indicates a specific
selected snapshot.
N
j
avguju
N
j
avgnjnavguju
II
IIII
K
1
2
,,
1
,,,, .
(18)
The following sections verify the proposed K
determination strategy using simulation and real measurement
data.
B. Simulation verification
In order to verify the analytical model and underlying
assumptions associated with the proposed method, simulations
were performed using the distribution system shown in Fig. 7
and the neutral network parameters given in Table I. A
2 MVA unbalanced load (1.0 MVA on phase A, 0.5 MVA on
phase B and 0.5 MVA on phase C) is placed at the end of the
feeder to represent primary system unbalance. At the low
voltage network, a 24-hour load behavior is simulated using
the method proposed in [15], which models the random house
consumption pattern. Fig. 8 presents currents Ia, Ib and In for a
single day simulation.
Feeder load
BA
C
Supply system
m n
Ia
Ib
RCRT
Rgn
N
In
XX X X
RT
zn
RG2
zp
Za,c2
Zb,c2
m
zp
zn,c2
zp,c2
zp,c2
RG1
Za,c1
Zb,c1
zn,c1
zp,c1
zp,c1
External
customer
Customer
under study
Iu
nZab,c2
Zab,c1
RgnRgs
Ig
In
Ib
Ia
External site
Supply
System
Feeder
Load
Fig. 7. Simulated network.
TABLE I
NEUTRAL NETWORK PARAMETERS
Parameters Values
Substation grounding impedance (Rgs) 0.15 Ω
Primary neutral grounding resistance (Rgn) 15 Ω
Impedance of primary feeder’s MGN 0.570 + j1.281 Ω/km
Grounding span of the primary feeder’s MGN 75 m
Transformer grounding resistance (RT) 15 Ω
Customer grounding resistance (RG1, RG2) 1 Ω
Impedance from transformer to PCC (zn) 0.0214 + j0.0480 Ω
Impedance from PCC to service panel 1 (zn,c1) 0.028 + j0.018 Ω/km
Impedance from PCC to service panel 2 (zn,c2) 0.165 + j0.110 Ω/km
0 5 10 15 200
20
40
I A (
A)
Time (h)
0 5 10 15 200
20
40
I B (
A)
Time (h)
0 5 10 15 200
10
20
I N (
A)
Time (h) Fig. 8. House current profile for a 24-hour simulation.
The algorithm proposed in Section IV.A is, then, applied to
the current profile of Fig. 8 in order to calculate the current
6
return ratio K. Obtained results, presented in Fig. 9, outline
that ratio K remains constant throughout the day, regardless of
the customer load configuration.
0 2 4 6 8 10 120
2
4
6
8
10
12
Iu (A)
In
(A
)
Measurement results
K = 0.8866
Fig. 9. Verification of K determination approach.
C. Measurement results
In order to verify the proposed methodology, field
measurements have been collected for different houses, with a
measurement period ranging from 3 to 15 days. The data
selection algorithm developed in Section IV.A is performed
and the obtained results are presented in Fig. 10, for two
different houses.
0 2 4 6 8 10 12 140
2
4
6
8
10
12
Iu (A)
In
(A
)
Measurement results
K = 0.8504
(a) house 1 (4-day data)
0 5 10 15 20 25 300
5
10
15
20
25
Iu (A)
In
(A
)
Measurement results
K = 0.6892
(b) house 2 (10-day data)
Fig. 10. Determination of current return ratio at 2 houses.
The selected measurement data fits quite well a straight
line on both houses, which indicates the proposed K ratio is,
in fact, constant during a multi-day measurement period.
A further detailed analysis of Fig. 10(a) may expose two
straight lines with slightly different slopes. Such result is
obtained since the current transformers used for measurements
on phases A and B are not exactly equal. This phenomenon
can be visualized in Fig. 11, where load operations on phase
A and on phase B have been split. One may notice, however,
that the difference between the two slopes is small and, for
practical purposes, can be neglected.
0 2 4 6 8 10 12 140
2
4
6
8
10
12
Iu (A)
In
(A
)
KA = 0.8557
KB = 0.8135
Fig. 11. Phase decoupling on the current return ratio estimation.
V. CHARACTERISTICS OF THE CURRENT RETURN RATIO
In this section, some sensitivity studies are performed to
address the impact of neutral circuit parameters on K ratio.
The following parameters are studied:
Customer grounding impedance (RG1);
Customer neutral impedance (zn,c1);
Primary grounding impedance (Rgn);
Neutral circuit parameters from other customers (RG2
and zn,c2).
A. Customer grounding impedance
On this study, the customer grounding impedance is
increased from 1 Ω to 15 Ω, while other parameters remain
the same as on the base case. Fig. 12 presents the simulation
result. It states that a larger grounding resistance increases the
current return ratio, since more current will flow through the
neutral conductor, instead of the grounding branch. An
infinite grounding impedance (open-circuit) would provide
K = 1; all unbalance current flows through neutral conductor
since there is no alternative path.
0 2 4 6 80.8
0.85
0.9
0.95
1
Customer grounding impedance ()
Cu
rre
nt
retu
rn r
atio
Fig. 12. Effect of customer grounding impedance on current return ratio.
B. Neutral conductor impedance (bad neutral condition)
According to Fig. 3, the returning neutral current is also
affected by the high resistance of the neutral conductor due to
deterioration or bad connections. To simulate a bad neutral
condition, a resistance is added in series with the neutral
impedance zn,c1 of Fig. 3 and a new simulation is performed.
Fig. 13 presents the results. K ratio is reduced from 0.88 to
0.67 when zn,c1 is increased, since larger impedance on neutral
path will bias a higher ratio of current unbalance towards the
grounding branch.
0 0.2 0.4 0.60.65
0.7
0.75
0.8
0.85
0.9
Additional resistance due to bad neutral ()
Cu
rre
nt
retu
rn r
atio
Fig. 13. Effect of neutral impedance on current return ratio.
C. Primary grounding impedance
The primary neutral grounding conditions can be examined
by varying the grounding resistance (Rgn). The effect of
7
changing just one or a few grounding resistances is not
significant in the primary neutral because a large number of
other grounding resistances dominate the effect. Therefore, all
the grounding resistances (Rgn) were varied. For the same
reason Rgs is not included on the sensitivity analysis.
The obtained sensitivity results are shown in Fig. 14. It
states that poor primary grounding conditions have negligible
impact on current return ratio K, even for large Rgn values
(i.e., 30 Ω). The slight change observed on K ratio is due to
the connection of customer and external grounding systems
through the earth. For practical purposes, this change can be
neglected, if compared to RG1 and zn,c1 impacts.
10 15 20 25 300.8
0.85
0.9
0.95
1
Primary neutral grounding resistance ()
Cu
rre
nt
retu
rn r
atio
Fig. 14. Effect of primary grounding characteristics on current return ratio.
D. Neutral circuit parameters from other customers
On this study, the impact of neutral circuit parameters of
external customers on ratio K is identified. Fig. 15 confirms
the conclusion previously obtained, stating that neutral circuit
parameters of the external circuit have negligible influence on
ratio K.
0 2 4 6 80.8
0.85
0.9
0.95
1
Customer grounding impedance ()
Cu
rre
nt
retu
rn r
atio
(a) RG2
0 0.2 0.4 0.60.8
0.85
0.9
0.95
1
Additional resistance due to bad neutral ()
Cu
rre
nt
retu
rn r
atio
(b) zn,c2
Fig. 15. Effect of other customer parameters on current return ratio.
VI. CONCLUSIONS
A nonintrusive measurement-based method to model the
NEV rise issue at the customer facility has been proposed in
this paper. The key feature of the method is the current return
ratio concept, which is calculated using a data selection
technique based only on phase and neutral currents measured
at the customer service panel. The K ratio is constant
regardless of the load connected to the network, since it only
depends on neutral circuit impedances. Sensitivity studies
have demonstrated that major parameters affecting K are the
customer grounding resistance and the impedance of the
neutral conductor connecting the customer under study to the
remaining network. An attractive characteristic of this method
relies on the fact K ratio calculation may be performed
without the need to artificially manipulate customer loads.
A promising application of this method consists on locating
and troubleshooting the possible causes of stray voltage
related incidents. It can easily quantify the different
contributions to NEV rise at the customer site. Such
application is described in a companion paper.
VII. APPENDIX
Considering the single-customer scenario, the current
return ratio K can be determined analytically, using the
following procedure. Initially, an equivalent low-voltage
network circuit, derived from Fig. 2, is considered. Such
circuit is presented in Fig. 16.
zn
RG
zp
Za
Zb
m
zp
nZab
+-
+-
Va
Vb
Iu
Ig
In
Ia
Ib
+-VNEV
ZMGN
Fig. 16. Low-voltage network for K ratio calculation.
The circuit is simplified applying the delta-wye
transformation to the load. The newly obtained network is
presented in Fig. 17, where the equivalent loads are given by
(19).
abba
aba
ZZZ
ZZZ
1 ;
abba
abb
ZZZ
ZZZ
2 ;
abba
ba
ZZZ
ZZZ
3
(19)
zn
RG
zp
m
zp
n
+-
+-
Va
Vb
Iu
Ig
In
Ia
Ib
+-VNEV
ZMGN
Z1
Z2
Z3
Fig. 17. Simplified low-voltage network for K ratio calculation.
The circuit may be further simplified by calculating the
Thévenin equivalent seen from nodes m and n. The obtained
equivalent circuit is presented in Fig. 18, where
12
12
ZzZz
VZzVZzV
pp
bpap
th
(20)
3
21
21Z
ZzZz
ZzZzZ
pp
pp
th
(21)
8
zn
RG
m n
+-
Zth- +
Vth
ZMGN
VNEV
Iu
Ig
In
Iu
Fig. 18. Equivalent low-voltage network for K ratio calculation.
Once Kirchhoff’s second law is applied to the lower mesh
of Fig. 18, the following equation is obtained
0 gGnngMGNNEV IRIzIZV
0 nnnuGMGNNEV IzIIRZV
nGMGN
NEVu
nGMGN
GMGNn
zRZ
VI
zRZ
RZI
(22)
Therefore, from (22), the K ratio is given by
nGMGN
GMGN
zRZ
RZK
(23)
The equivalent primary neutral impedance ZMGN is
calculated using the method proposed in [7].
VIII. REFERENCES
[1] J. Burke, “The Confusion Over Stray Voltage,” IEEE Ind. Applications
Mag., vol. 14, no. 3, pp. 63-66, May/Jun. 2008.
[2] J. Hultgren, “Small electric currents affecting farm animals and man: A
review with special reference to stray voltage,” Veterinary Research
Communications, vol. 14, no. 4, pp. 287-298, Jul. 1990.
[3] K. Dosier, and J. Burke, “Stray Voltage Issues,” in Proc. 2006 IEEE
PES Transmission and Distribution Conference and Exhibition, pp.
247-250.
[4] D. W. Zipse, “The Hazardous Multi-Grounded Neutral Distribution
System and Dangerous Stray Currents,” in Proc. 2003 IEEE Petroleum
and Chemical Industry Committee Technical Conference, pp. 1-23.
[5] S. Chan, “Con Ed Finds 1,214 Stray Voltage Sites in One Year,” The
New York Times, New York, USA, 2006. [Online]. Available:
http://www.nytimes.com/2006/03/04/nyregion/04voltage.html?ex=129
9128400&en=f53afd789fa5445f&ei=5090&partner=rssuserland&emc
=rss.
[6] IEEE Working Group, Voltages at Publicly and Privately Accessible
Locations, Trial Use Guide (Draft), 2009.
[7] J. R. Acharya, Y. Wang, and W. Xu, “Temporary Overvoltage and GPR
Characteristics of Distribution Feeders With Multigrounded Neutral,”
IEEE Trans. Power Del., vol. 25, no. 2, pp. 1036–1044, Apr. 2010.
[8] S. Patel, and F. Lambert, “Induced Stray Voltages from Transmission
Lines,” in Proc. 2006 IEEE Transmission and Distribution Conference
and Exposition, pp. 254-259.
[9] A. M. Lefcourt, Effect of Electrical Voltage/Current on Farm Animals,
US Department of Agriculture, Handbook No. 196, 1991, p. 152.
[10] P. E. Ortmann, “Recent Developments in Stray Voltage Rules and
Regulations,” in Proc. 2006 IEEE Rural Electric Power Conference,
pp. 1-4.
[11] T. C. Surbrook, J. R. Althouse, and K. G. Tinsey, “Protocols and
Practices for Stray Voltage Testing,” in Proc. 2003 Stray Voltage and
Dairy Farms, pp. 521-542.
[12] R. S. Reines, and M. A. Cook, “Measurement Protocols and Data
Acquisition Processes for Stray Voltage Investigation,” in Proc. 2003
Stray Voltage and Dairy Farms, pp. 230-247.
[13] M. A. Cook, D. M. Dasho, and R. S. Reines, “On Distinguishing
Various Contributors to Stray Voltage from Both ‘On-Farm’ and ‘Off-
Farm’ Sources,” PSC Wisconsin – White Paper Series, Mar. 1994.
[14] A. Charette, and G. Simard, “Stray Voltage at Farm Site – Utilities
Practice and Review,” in Proc. 2006 IEEE PES Transmission and
Distribution Conference and Exhibition, pp. 260-262.
[15] D. Salles, C. Jiang, W. Xu, W. Freitas, and H. E. Mazin, “Assessing the
collective harmonic impact of modern residential loads—Part I:
Methodology,” IEEE Trans. Power Del., vol. 27, no. 4, pp. 1937-1946,
Oct. 2012.
IX. BIOGRAPHIES
Wilsun Xu (M’90-SM’95-F’05) obtained the Ph.D. from the University
of British Columbia, Vancouver, in 1989. Currently, he is a Professor and a
NSERC/iCORE Industrial Research Chair at the University of Alberta. His
current research interests are power quality and information extraction from
power disturbances.
Ricardo Torquato (S’11) obtained the B.Sc. degree in electrical
engineering from the University of Campinas, Campinas, Brazil in 2011,
where he is pursuing a M.Sc. degree. At present, he is a visiting student at
the University of Alberta. His research interests are power quality, analysis of
distribution systems and distributed generation.
Diogo Salles (S’04-M’12) received the B.Sc., M.Sc. and Ph.D. degrees,
all in electrical engineering, from the University of Campinas, Campinas,
Brazil, in 2006, 2008 and 2012, respectively. Currently, he is a Post-Doctoral
Researcher at the University of Campinas. From 2010 to 2012, he was a
Visiting Doctoral Scholar at the University of Alberta, Edmonton, AB,
Canada. His research interests focus on power quality, harmonics and power
disturbance data analysis.
1
Abstract — Stray voltages have always been a concern to
utility companies and customers. But methods to troubleshoot
and monitor stray voltage problems are very limited. This paper
presents a passive, measurement based method to identify the
contributors to the common cause of stray voltages, the neutral-
to-earth voltage (NEV) rise at the service entrance point. The
paper shows that the NEV can be decoupled into two
components, those related to the customer under investigation
and those outside the customer facility. A method to quantify the
relative contributions of the two components is proposed. A new
concept called current return ratio is introduced to facilitate the
decoupling and to quantify the grounding conditions of the
system. This paper presents the background, circuit model,
concept and theory of the proposed method.
Index Terms—Power quality, stray voltage, neutral-to-earth
voltage.
I. INTRODUCTION
TRAY voltage is a voltage present between two
conductive surfaces that can be simultaneously contacted
by a human or animal. It has been an issue to farm livestock
for many years since animals are more susceptible to stray
voltages [1]-[5]. In recent years, complaints of stray voltage
problems involving humans have become more frequent [1],
[6], partially due to increased awareness of the problem and
the use of various new loads by customers. Utility companies
and some of their customer groups have become increasingly
interested in tools that can help to troubleshoot stray voltage
problems.
Among the various causes of stray voltages, the neutral-to-
earth voltage (NEV) at the customer-utility interface point is
the main cause [7]. A high NEV can arise due to unbalanced
single-phase loads; excessive neutral current in the primary
feeder; high resistance in neutral conductor; or poor
grounding at the primary feeder, etc. [8]-[10]. Due to the
existence of many sources of NEV, it is important to
This work was partially supported by the Natural Sciences and
Engineering Research Council (NSERC), Canada and by the São Paulo
Research Foundation (FAPESP), Brazil.
W. Xu, J. Acharya and R. Torquato are or were with the Department of
Electrical and Computer Engineering, University of Alberta, Edmonton, AB
T6G 2V4, Canada (email: [email protected]; [email protected]).
J. Yong is with the State Key Laboratory of Power Transmission
Equipment and System Security and New Technology, Chongqing
University, Chongqing, 400044, China (email: [email protected]).
determine first whether a high NEV situation is caused by
customer loads or by factors external to the customer facility.
This information will be very helpful to formulating proper
troubleshooting strategies and establishing responsibilities for
the parties involved.
To our best knowledge, a proper and easy-to-use tool for
NEV source detection at the utility-customer interfacing point
is still not available at present. Many jurisdictions in the US
and Canada have been practicing stray voltage investigation
protocols in order to determine the causes of stray voltages,
especially the NEV rises [2], [11]-[14]. These protocols have
some common limitations. Firstly, they are quite intrusive.
Some require adding one or more proxy loads to the circuit
[11]-[13]. Others require operating customer loads in certain
ways during troubleshooting [14]. A complete disconnection
of customer loads is also proposed in [15], which isolates the
utility contribution to NEV. Secondly, the procedures require
to measure the NEV, which means a reference zero-potential
point must be created. This task can be difficult to complete
properly and, sometimes, cannot be done. The results could be
affected by the quality of the reference ground as well. In
summary, the available NEV source finding techniques are
still far from meeting the requirements of industry.
This and a companion papers present a NEV source and
cause determination method developed through several years
of effort at the University of Alberta. The proposed method is
a passive monitoring technique implemented at the service
entrance point, without interfering with customer operations.
Furthermore, it does not require measuring the NEV directly,
thereby eliminating the need for creating a reference ground.
The results could significantly narrow down the scope of
troubleshooting. In addition, the technique makes it possible
to conduct nonintrusive monitoring of the NEV conditions
over an extended period such as several months.
This paper is organized as follows. Section II explains the
mechanism of NEV rise including the network model for its
analysis. Section III establishes the concept of current return
ratio. This concept is central to the proposed method. A
measurement based method to determine the ratio is also
presented. Section IV presents the method to determine the
relative contributions to NEV by customers and external
sources. Section V summarizes the overall NEV monitoring
method.
A Method to Determine Stray Voltage Sources
– Part I: Concept and Theory (Final Version)
Wilsun Xu, Fellow, IEEE, Janak R. Acharya, Ricardo Torquato, Student Member, IEEE, and Jing
Yong, Member, IEEE
S
2
II. THE NEUTRAL-TO-EARTH VOLTAGE (NEV) PROBLEM
A. The Phenomena of Neutral-to-Earth Voltage Rise
A typical North American secondary system is shown in
Fig. 1. The Neutral-to-Earth Voltage (NEV) for customer of
house #1 is defined as the voltage of node n with respect to a
remote earth point. Ideally, this voltage should be zero from
the perspective of electrical safety. However, due to various
factors explained later, it is often not zero. If this voltage is
sufficiently high, stray voltage incidents may occur, as
follows: The neutral point n is always bonded to the metal
structures such as water pipes of the customer facility. High
NEV implies that those structures become “energized”, i.e.
experiencing elevated potential. If a person touches such a
structure, electrical sensation may occur. Swimming pool is a
common place encountering such a NEV problem [1]. When
entering or exiting a swimming pool, a person may
simultaneously contact the pool sidewalk or water (at ground
potential) and the metallic ladder (which is bonded to neutral
n). The human body will then experience the NEV. A tingling
sensation may happen due to current flowing through the
body. General public considers such events as a voltage
having “strayed” to the swimming pool.
nHouse
#1
House
#mGmR
G2R
RG1
House
#2
Customer under
study
zp,c1
zn,c1
zp,c1
zp,c2
zn,c2
zp,c2
zp,cm
zn,cm
zp,cm
In,c1
Ig1A
B
N
In
Ib
Ia
zp
zn
zp
APCC
BPCC
NPCC
NEV
TR
One
phas
e co
nduct
or
Pri
mar
y n
eutr
al c
onduct
or
Rgn
3-phase 4-wire
primary network
Fig. 1. Typical North American low voltage network.
According to the figure, the NEV is caused by the current
Ig1 entering the customer side grounding resistance RG1. For
example, if there is an excessive neutral current (In,c1)
returning from the customer facility, part of this current can
flow through RG1 and the NEV will rise. In another case, if the
neutral conductor connecting customer and utility is broken or
poorly connected, more customer neutral current will flow
through RG1 and NEV will also rise. If the customer grounding
is poor (i.e. large RG1 value), NEV will rise as well.
Alternatively, if the supply system has a high neutral voltage
at point N, this voltage can propagate to the RG1 location,
leading to higher NEV. The high neutral voltage at point NPCC
which could be created by other customers may also
propagate to point RG1, causing higher NEV.
B. Circuit Model for NEV Analysis
The secondary network for NEV study requires a
multiphase network model as shown in Fig. 2 (only one
customer is shown in the figure). Such a model is necessary to
accurately represent the system neutral and grounding
conditions, in addition to modeling the load unbalance within
the customer’s facility. As shown in the Figure, customer
loads may be connected in the forms of phase-to-neutral or
phase-to-phase. According to the code, a customer’s facility
has only one grounding point which is n, located at the service
entrance point (or service panel). There is no additional
grounding point within the facility.
The primary system interconnects with the customer
facility through a single-phase, three-winding transformer.
There are two connection points, phase node Aprim and neutral
node Nprim. As such, the primary system is modeled as a two-
port equivalent network with two equivalent voltage sources.
One source (Vprim_ph) connects to the phase conductor through
node Aprim and represents the supply voltage. The voltage
source Vprim_n represents the voltage present at the primary
neutral point and it connects to the facility through node Nprim.
This voltage models the neutral voltage rise caused by the
upstream system and loads. A service feeder consisting of 2
hot and 1 neutral conductors connects the service transformer
with the customer facility.
The customer location has a grounding resistance of RG.
The service transformer has a grounding resistance of RT.
RT
zn
RG
zp
Za
Zb
zp a
Zab
Iu
- +
Vprim_ph Zprim_ph
- +
Vprim_n Zprim_n
Customer
n
b
A
N
B
In
Ib
Ia
External site
Ig
Service panel
Aprim
Nprim
Fig. 2. Low voltage network model used to analyze the NEV behavior.
According to the circuit, the neutral-to-earth voltage, NEV,
on a customer site can be determined as follows:
nuGgGn IIRIRVNEV (1)
The above relationship reveals that Vn is influenced by the
unbalanced load current Iu and the current on the service
neutral conductor, In. Therefore, the customer NEV is caused
by two contributing factors, namely the customer and the
external contributions. The customer contribution arises from
the load unbalance at the customer site. In such a situation,
Iu ≠ 0 and part of Iu flows to the ground, causing the NEV rise.
3
The external contribution is related to the neutral voltage rise
at the PCC (i.e. the node N). This voltage rise can be caused
by unbalanced loads and/or grounding problems in the
primary network, the secondary network and other customers
in the neighborhood. These factors can be understood as a
non-zero equivalent voltage source Vprim_n. Through the
neutral connection, this source can cause a current flowing
into the customer neutral, leading to a higher NEV.
Another useful property revealed by Eqn. (1) is that the
NEV is in proportion to the ground current Ig. Therefore, if
the contributors to Ig can be determined, the factors creating
NEV can also be determined. The goal of the proposed
method is to determine the relative contributions to Ig due to
the customer load unbalance and to the factors external to the
customer facility. Using this strategy, the requirement to
establish a reference potential point for NEV measurement is
eliminated.
III. THE CURRENT RETURN RATIO
In order to determine the relative contributions of the
customer and external causes to the NEV, a new concept
called the current return ratio needs to be established first.
According to Fig. 2, the unbalanced current produced by the
customer loads (Iu) returns to the primary system either
through the neutral conductor (In) or through the grounding
branch (Ig). This research shows that the neutral current In is
related to the unbalanced load current Iu through the following
relationship:
neun IIKI (2)
where K is defined as the Current Return Ratio, Ine is the
current caused by external factors unrelated to the customer
load. The current return ratio can be understood as the
percentage of the unbalanced load current that returns to the
supply system through the service neutral conductor.
A. Current Return Relationship for a Simplified System
In this section, we will use a simplified residential circuit
to demonstrate that the above relationship does exist. It will
also reveal that K is a function of the network impedance
parameters only. Therefore, it is a constant if the impedance
parameters don’t change. A rigorous mathematical proof of
the relationship is presented in the Appendix.
Fig. 2 can be further simplified to Fig. 3. Voltage sources
Va and Vb represent the supply system on the low voltage side
of the interconnection transformer. The neutral network
upstream of and including RT can be simplified as a Thévenin
equivalent (VMGN and ZMGN). ZMGN is approximately equal to
the parallel impedance of Zprim_n and RT in Fig. 2. The supply
system feeds the customer through two hot and one neutral
conductor, with impedances zp and zn, respectively. The
customer facility is represented by phase-to-neutral (Za and
Zb) and phase-to-phase (Zab) connected loads and the neutral
point is grounded through the resistance RG.
zn
RG
zp
Za
Zb
m
zp
nZab
+-
+-
Va
Vb
Iu
Ig
In
Ia
Ib
+-
VMGN
ZMGN
Fig. 3. Simplified residential circuit to determine K ratio.
To determine the relationship between neutral current In
and unbalanced load current Iu, the circuit is further simplified
using the delta-wye transformation to the load. The newly
obtained network is presented in Fig. 4, where the equivalent
loads are given by (3).
abba
aba
ZZZ
ZZZ
1 ;
abba
abb
ZZZ
ZZZ
2 ;
abba
ba
ZZZ
ZZZ
3
(3)
zn
RG
zp
m
zp
n
+-
+-
Va
Vb
Iu
Ig
In
Ia
Ib
+-
VMGN
ZMGN
Z1
Z2
Z3
Fig. 4. Residential circuit after delta-wye transformation on the load.
The circuit is rearranged next as in Fig. 5(a) and a
Thévenin equivalent is calculated for the circuit portion
circled in red (between nodes m and n). The obtained
equivalent circuit is presented in Fig. 5(b), where
12
12
ZzZz
VZzVZzV
pp
bpap
th
(4)
3
21
21Z
ZzZz
ZzZzZ
pp
pp
th
(5)
Once Kirchhoff’s second law is applied to “Mesh α” of the
resulting circuit, the following relationship is obtained:
4
0 gGnngMGNMGN IRIzIZV (6)
zn
RG
Z3
m n
+-
Z1 + zp- +
Va
ZMGN
VMGN
Z2 + zp+ -
Vb
Iu
Ig
In
Ia
Ib
(a)
zn
RG
m n
+-
Zth- +
Vth
ZMGN
VMGN
Iu
Ig
In
Mesh α
(b)
Fig. 5. Equivalent low-voltage network for K ratio calculation.
Substituting the ground current (Ig) by Iu - In, (6) may be
rearranged to isolate the neutral current, as follows
0 nnnuGMGNMGN IzIIRZV (7)
nGMGN
MGNu
nGMGN
GMGNn
zRZ
VI
zRZ
RZI
(8)
Equation (8) is in the form of (2), and the K ratio can be
determined by (9). Using typical data of RG = 1 Ω,
zn = 0.17 +j 0.11 Ω, and ZMGN = 0.52 + j0.32 Ω, gives
K = 0.89 – j0.04. Typical values of K are estimated as from
0.85 to 0.95.
nGMGN
GMGN
zRZ
RZK
(9)
B. Multi-customer Circuit and Three-phase Systems
The proposed current return ratio concept is also
applicable for the multi-customer network. To apply the
proposed concept, other houses connected to the LV circuit
are included as an external contribution to the NEV rise of the
customer under study, as presented in Fig. 6.
The current return ratio concept is equally applicable to
three-phase 4-wire loads such as the one presented in Fig. 7.
The unbalanced current required for the proposed method can
be obtained by using the three line currents as in (10).
Compared to the single-phase system, the three-phase
configuration requires an extra current probe. The study of
both configurations involves the same procedure, so a
separate study is not essential for a three-phase system.
cbau IIII (10)
RT
zn
RG2
zp
Za,c2
Zb,c2
zp
zn,c2
zp,c2
zp,c2
RG1
Za,c1
Zb,c1
zn,c1
zp,c1
zp,c1
Iun
Zab,c2
Zab,c1
- +
Vprim_ph Zprim_ph
- +
Vprim_n Zprim_n
a
b
Ig
In
Ib
Ia
Customer
External site
A
B
N
Aprim
Nprim
Fig. 6. Multi-customer network model for understanding K ratio.
RT RC
Primary circuit Secondary circuit
Interconnection In
Ia
Ib
Ic
RTRG
Primary circuit Secondary circuit
Interconnection
Fig. 7. Three-phase customer supplied from a MGN system.
C. Measurement Method to Determine K
In practice, the K ratio is impossible to calculate because it
depends on circuit impedances whose values are not available.
This section presents a measurement-based approach to
determine the K ratio.
Eqn. (2) represents the relationship among K, In, Iu and Ine.
In and Iu can be measured at the service entrance point. Iu
equals Ia + Ib, as the customer has only one grounding point
(point n in the figure). However, Ine cannot be measured
directly.
To determine the current return ratio, equation (2) is
applied to two sets of measurement data, extracted from
consecutive instants of time, as follows:
111 neun IKII , for data measured at first instant (t1) (11)
222 neun IKII , for data measured at second instant (t2) (12)
Subtracting (12) from (11) yields
121212 neneuunn IIIIKII
neun IIKI (13)
5
In order to estimate the ratio K from (13), the external
current variation (ΔIne) must be very small compared to the
variation of the unbalanced current (ΔIu). Otherwise, the
influence of external neutral current will result in inaccuracies
in K value. To minimize such an influence, two requirements
must be fulfilled. Firstly, only data sets collected during
changes of the current unbalance (Iu) should be used.
Secondly, one should use a small interval (such as less than 1
second) between two collected snapshots, which minimizes
the probability of changes in the external system. Once these
requirements are satisfied, ∆Ine can be neglected in
comparison with ∆In and ∆Iu, which yields,
u
n
I
IK
(14)
As residential neutral circuits are mostly resistive,
experiments have shown that the real part of K ratio is much
higher than its imaginary part. Therefore, for practical
purposes, only the magnitudes of current changes may be
considered.
In practice, K is obtained from a large amount of current
change snapshots selected over a measurement period of
several hours or even days. A power fluctuation source
identification method of [16] is applied for selecting the
proper data points. The resulting dataset, composed of N
selected snapshots, associates ΔIu and ΔIn as shown in (15).
Nu
iu
u
u
Nn
in
n
n
I
I
I
I
K
I
I
I
I
,
,
2,
1,
,
,
2,
1,
(15)
Applying least square fitting method to the above equation,
the coefficient K can be solved and the solution is shown in
Eqn. (8). In this equation, ΔIu,avg and ΔIn,avg are, respectively,
the average of ΔIu and ΔIn over the N selected snapshots; and
the subscript i indicates a specific selected snapshot.
N
i
avguiu
N
i
avgninavguiu
II
IIII
K
1
2,,
1
,,,, .
(16)
Verification of the above measurement-based method for K
ratio determination and its performance characteristics will be
presented in the companion paper. The relationship revealed
in (2) has important applications. Extensive sensitivity studies
on the characteristics of K and the associated applications are
also presented in the companion paper. In the following
section, the concept is applied to decouple customer and
external contributions to the NEV.
IV. RELATIVE CONTRIBUTIONS TO NEV
As previously stated in Section II and Section III, both
neutral current In and ground current Ig can be divided into
two components, as presented in (17) and (18). Inc and Ine are,
respectively, the customer and external components of the
neutral current, while Igc and Ige are, respectively, the
customer and external components of the ground current. The
negative sign in (17) has been chosen since customer and
external contributions to neutral current interact in opposite
directions (i.e., customer contribution flows from customer to
the external site, while external contribution flows on the
opposite way). On the other hand, both contributions to
ground current flow from point n to the ground.
nencn III (17)
gegcg III (18)
By comparing (2) to (17), customer contribution to the
neutral current is given by
baunc IIKKII (19)
Part of the unbalanced load current Iu returns to the
external site through the neutral conductor (Inc) and the
remaining current returns through the customer grounding
point (Igc). Therefore, Iu = Inc + Igc, and the customer
contribution to ground current is given by
bauncugc IIKIKIII 11 (20)
From Fig. 2,
nug III (21)
By replacing (20) and (21) into (18), Ige can be determined
as follows
nbagcnugcgge IIIKIIIIII (22)
The ground current components can be plotted as shown in
Fig. 8. The percentage contribution of the customer can be
determined by a projection of Igc on Ig, as follows
%100
cos1%100
cos11
nu
u
g
gc
cII
IK
I
IF
(23)
6
Likewise, the percentage contribution of the external site is
%100cos
%100cos
22
nu
nu
g
ge
eII
IKI
I
IF
(24)
δ1
δ2
Igc = (1 – K)Iu
Customer component
Fig. 8. Phasor diagram of ground current components.
According to (23), if K = 1 or Iu = 0, contribution factors
Fc = 0 and Fe = 100%. These results mean that when either all
the customer load current returns through the neutral
conductor or the customer loads are balanced, the external site
(utility and other customers) is fully responsible for the NEV
rise at the customer facility. Similarly, if K = 0 which may
represent the case of a broken secondary neutral In = 0, Fe = 0
and Fc = 100%, i.e., the customer is technically responsible
for the NEV rise. (But a broken neutral conductor may be the
responsibility of the utility. This issue will be addressed in the
companion paper). In reality, 0 < K < 1 and Iu ≠ 0. Therefore,
both customer and external contributions do exist.
As explained earlier, NEV is in proportion to Ig through a
constant impedance Rg. The relative contribution factor to Ig
is, therefore, applicable to NEV. In this work, Fc and Fe are
called contribution factors to NEV.
V. SUMMARY OF THE NEV MONITORING METHOD
A complete implementation of the proposed NEV
contributor determination method, through a dedicated device
or a power quality monitor, is shown in Fig. 9 and
summarized as follows.
b
a
n
b a n
Water pipe
Metal
structure
Service drop
Ground rod
Ser
vic
e p
an
el
2-ph load
TV
cable
1-ph load
Stray Voltage
monitor
Current
probes
Fig. 9. Layout of the service panel with the stray voltage monitor.
The device or monitor must have three current sensors that
sense the currents Ia, Ib and In at the service entrance point. A
sampling rate of 64 points per cycle is sufficient for
fundamental frequency NEV monitoring. The monitoring shall
be performed for at least one week. It can be longer
depending on the troubleshooting need. The sample current
waveforms are processed to extract the fundamental frequency
components. The method to determine NEV contributions is
then applied. The K ratio and the contribution factors can be
output from the device/monitor at a resolution, say, around
one result per one minute. The overall algorithms are shown
in a high-level flowchart presented in Fig. 10.
Determine K using method described in Section III.C
Measure currents Ia, Ib and In at customer service panel for desired
period of time, and apply FFT to extract 60 Hz currents
Determine percentage contributions to NEV (Fc and Fe) using:
%100
cos1 1
nu
u
cII
IKF
%100cos 2
nu
nu
eII
IKIF
Determine contributions to ground current (Igc and Ige) using:
nbage IIIKI
bagc IIKI 1
Fig. 10. Flowchart of the overall NEV contributor determination method.
VI. CONCLUSIONS
A passive, measurement-based, method to determine the
contributors to a customer’s neutral-to-earth voltage has been
presented in this paper. The method decouples the NEV rise
into two factors, one is related to the customer loads and the
other is related to the supply system or neighboring loads.
This decoupling is made possible through two concepts. The
first one is to decouple the NEV indirectly through decoupling
the current flowing into the customer ground. This approach
eliminates the difficult task of establishing a reference ground
for NEV measurement. The second concept is the current
return ratio K. This concept has shown that it is possible to
decouple the ground current into the customer-related portion
and the external-related portion. The current return ratio can
measure the quality of grounding conditions, as it only
depends on circuit and grounding impedances. A simple
measurement based method has been developed to determine
the current return ratio. Another contribution of this paper is
the introduction of a comprehensive multiphase circuit model
for NEV analysis and interpretation. The verification and
application of the proposed method will be presented in a
companion paper.
VII. APPENDIX
To demonstrate the K relationship for a multi-customer
circuit, a generic low voltage network is presented in Fig. 11.
7
Matrix [Z]equivalent represents the equivalent impedance of the
supply system and other neighbor customers. Vph_A and Vph_B
are the voltage sources of the energized phases, while Vneutral
is the voltage source of the neutral circuit.
- +
Vph_A
- +
Vph_B
- +
Vneutral zn
RG
zp
zp
Iu Customer
under study
nIn
Ib
Ia
[Z]equivalentIg
A
N
B
Service panel
Supply system
+
other customers
Fig. 11. Generic network to demonstrate the K relationship.
According to nodal voltage theory, the current and voltage
conditions of a network such as the one presented in Fig. 11,
can be derived from the network nodal voltage
TNBnN VVVVV 21V (25)
where NB is the number of nodes in the network. As the
transformer is modeled by its admittance matrix, the circuit is
linear, composed solely by independent voltage sources and
impedances.
From the network presented in Fig. 11, the neutral current
(flowing between points N and n) and the ground current
(flowing from point n towards the ground) can be written as a
function of the nodal voltages as in (26) and (27).
nNn VVfI , (26)
nung IIVgI (27)
As the impedance between points N and n is zn, the neutral
current may be written as:
n
Nnn
z
VVI
(28)
The ground current is proportional to the grounding
impedance RG and can be determined as in (29).
G
ng
R
VI (29)
By isolating Vn in (29) and substituting it in (28), the
resulting equation is
N
n
g
n
Gn V
zI
z
RI
1 (30)
Voltage VN can be further divided into a contribution from
the external site (named Vext) and another contribution from
the secondary network (Vsec) proportional to Ig, since it returns
to the external site through the ground return path. Therefore,
VN may be written as in (31), where A is a constant
determined by neutral circuit impedances.
gextextN IAVVVV sec (31)
By substituting (31) in (30), the neutral current can be
determined as:
ext
n
g
n
Gn V
zI
z
ARI
1 (32)
Finally, if (27) is substituted into (32), a relation between
neutral current In and customer unbalanced current Iu may be
derived as follows
ext
n
nu
n
Gn V
zII
z
ARI
1 (33)
ext
nG
u
nG
Gn V
zARI
zAR
ARI
1 (34)
nencneun IIIIKI (35)
In (35), K is the current return ratio, Inc is the contribution
of the customer to In and Ine represents the external
contribution to In.
VIII. REFERENCES
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IX. BIOGRAPHIES
Wilsun Xu (M’90-SM’95-F’05) obtained the Ph.D. from the University
of British Columbia, Vancouver, in 1989. Currently, he is a NSERC/iCORE
Industrial Research Chair Professor at the University of Alberta. His current
main research interests are power quality and power disturbance analytics
Janak R. Acharya received the B.Sc. degree in electrical engineering
from Tribhuvan University, Nepal, in 2002, the M.Sc. degree in electrical
engineering from the University of Saskatchewan, Saskatoon, SK, Canada, in
2005, and the Ph.D. degree in electrical engineering from the University of
Alberta, Edmonton, AB, Canada in 2010. At present, he is an engineer at the
ATCO Electric Ltd of Edmonton.
Ricardo Torquato (S’11) obtained the B.Sc. degree in electrical
engineering from the University of Campinas, Campinas, Brazil in 2011,
where he is pursuing a M.Sc. degree. At present, he is a visiting student at
the University of Alberta. His research interests are power quality, analysis of
distribution systems and distributed generation.
Jing Yong (M’08) received the B.Sc., M.Sc., and Ph.D. degrees from
Chongqing University, China, in 1985, 1988, and 2007, respectively, all in
electrical engineering. At present, she is a professor at Chongqing University,
China, and visiting professor at University of Alberta, Canada. Her research
interests are analysis of power distribution system and power quality.